Matrix eigenvalues ?

Question

201 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-01-01T21:38:11

See below.

Given #T = ([-1, 2, 2],[2, -1, 2],[2, 2, -1])#

the linear transformation eigenvalues are the #lambda#'s such that

#T x = lambda x# or

#(T-lambda I)x = 0#

This linear system has non null solutions when

#det(T-lambda I) = 0# relationship which determines the feasible eigenvalues.

Now #det ([-1-lambda, 2, 2],[2, -1-lambda, 2],[2, 2, -1-lambda]) = 0# is

#27 + 9 lambda - 3 lambda^2 - lambda^3 = 0# or

#(lambda-3)(lambda+3)^2=0# so the eigenvalues are

#lambda = {(3),(-3):}#